Does semantic evolution really go ‘From time to space’, as Haspelmath (1997), among others, suggests? Our purpose here will be to investigate the mechanisms underlying this particular semantic channel, with a corpus study of the French preposition après from the 11th to the 16th century. We first expose the issues of semantic evolution and universals, showing the opposition between the localist and cognitivist points of view. We describe the grammaticalization of après from Latin ad pressum, and show that the number of prepositions expressing time in Latin seems to suggest that the original meaning is not temporal, a hypothesis which our corpus study corroborates. We then expose our method, our corpus, and illustrate the meanings of the preposition après in Old and Middle French. The temporal meanings of après appear in the first French texts, along with spatial meanings: even though most dictionaries date the latter from the 12th century, our study shows that they appeared earlier - at the same time as the temporal meanings. The graph of après’s semantic evolution drawn from our corpus, and projected ‘backwards’, confirm the hypothesis of space-to-time evolution: après is thus a perfect illustration of Haspelmath’s principle, which enables us, through our study, to see the details of the processes involved in this phenomenon (invited inferencing), and to illustrate the gradualness of semantic evolution.